Rinnai tankless hot water heaters are well known in the World. This is a result of their long and successful history. founded in Japan in 1920, they have been making these units for a long time!
Their legacy, in other words, is quality and experience. If you buy a unit from a company with a long established reputation, you should fairly expect a product that works well and incorporates many generations of product tweaking and perfecting.
Rinnai tankless water heaters therefore do all the things that so impress people who switch from water heating tanks to tankless systems - they are compact (Rinnai describe one of their key products as the size of a bread box), they are quick to heat the water, and they can heat it for ever. Constant running hot water with no danger of running out.
The thing to look out for when deciding on tankless waterheaters is how much water they can heat at any one time, and whether that is going to be enough. So if you have three bathrooms with shower units and all are regularly used at the same time, then you need your water heater to be able to heat sufficient quantities.
The capacity of gas tankless water heaters is given in gallons per minute - the Rinnai Tankless Continuum, for example, can heat 8.5 gallons per minute. If the three showers in the above scenario are new, low usage, heads, then each will use 2 gallons, making a total of 6 gallons - well within the capacity. Older shower heads can use more water - up to 3.5 gallons per minute - so it is important that you do your calculations before you buy!